Orbital Alignments: An Exoplanet Diagnostic Tool

by Paul Gilster on August 31, 2007

The Rossiter-McLaughlin effect is an evolving tool for exoplanet research, one that has already begun to pay off. We recently looked at a paper studying whether this quirk of radial velocity methods could help in the detection of a terrestrial-class planet. The effect causes a distortion in radial velocity data during a planetary transit, one that seems to indicate a change in the velocity of the star under study. But in reality there is no change — what observers see is the effect of the transiting planet on the starlight, as shown in the diagram below.

It turns out the effect might be useful in finding planets larger than two Earth radii, but perhaps less so with smaller worlds. However, new work by a Japanese/American team using the Subaru Telescope points to a different observational capability. Observing the extrasolar system TrES-1, the team has been able to measure the angle between the parent star’s spin axis and the planet’s orbital axis, only the third time such an alignment has been measured.

Image: The Rossiter-McLaughlin effect is defined as the radial velocity anomaly during a transit from the known Keplerian orbit caused by the partial occultation of the rotating stellar disk. For example, if a planet occults part of the blue-shifted (approaching) half of the stellar disk, then the radial velocity of the star will appear to be slightly red-shifted, and vice-versa. The radial velocity anomaly depends on the trajectory of the planet across the disk of the host star, and in particular on the spin-orbit alignment of the system. Thus by monitoring the Rossiter-McLaughlin effect one can measure the spin-orbit alignment. Credit: National Astronomical Observatory of Japan.

TrES-1, a K0 star with a visual magnitude of 12, is the faintest target ever used in such work; its planet TrES-1b is a ‘hot Jupiter’ with an orbital period of three days. The outcome is welcome considering that ongoing transit surveys often work with faint stars indeed. In fact, we’re getting more and more interested in M-dwarfs in a variety of ways (especially in an astrobiological sense), knowing that the dim red objects may help us snare transits of objects of Earth’s size and even smaller. Now we have a way to measure spin/orbit alignments, allowing the collection of further data by which to study planet formation.

Ponder this: Given the preponderance of Jupiter-class worlds close to their parent stars that has emerged from early radial-velocity work, we’d like to know more about how they formed. Migration inward through the early solar system seems a reasonable assumption. Planets that form and migrate like this ought to show relatively minor misalignments between the stellar spin axis and the planet’s orbital axis.

Image: An illustration of the concept of the spin-orbit alignment (described by lambda) in an exoplanetary system. Credit: National Astronomical Observatory of Japan.

But planets dispersed by the gravitational effects of giant planets (‘planet-planet scattering’) through a protoplanetary disk should show tilts different from the original orbital axis. If such mechanisms are in play in a given system, measuring the spin/orbit alignment through the Rossiter-McLaughlin effect should reveal the resultant misalignment. That makes this tiny observational twist a genuine diagnostic tool in the continuing development of planet formation theories.

What’s next is surely to tighten up the numbers. The current study can only show an alignment angle of 30 degrees with an error of plus or minus 21 degrees. These are useful contraints (enough to demonstrate the prograde orbital motion of TrES-1b), but they’ll be refined with future work. The paper is Narita et al., “”Measurement of the Rossiter–McLaughlin Effect in the Transiting Exoplanetary System TrES-1,” Publications of Astronomical Society of Japan, Vol 59, No. 4 (August 25, 2007), pp. 763-770, available here.

Since the orbital planes must intersect, perhaps you can select an eccentric orbit that passes near the various nodes. It could take many orbits, but over time you’d get near to all of the planets in the system. The trick is selecting the optimum path, but you do it only once. If my understanding is correct, Cassini does something similar among Saturn’s moons. It may also be possible to spend a modest amount of fuel to later adjust the satellite’s orbit to create and visit other nodes if any one orbit doesn’t do everything that’s wanted.

Abstract: Instrumental projects that will improve the direct optical finding and characterisation of exoplanets have advanced sufficiently to trigger organized investigation and development of corresponding signal processing algorithms. The first step is the availability of field-of-view (FOV) models. These can then be submitted to various instrumental models, which in turn produce simulated data, enabling the testing of processing algorithms. We aim to set the specifications of a physical model for typical FOVs of these instruments.

The dynamic in resolution and flux between the various sources present in such a FOV imposes a multiscale, independent layer approach. From review of current literature and through extrapolations from currently available data and models, we derive the features of each source-type in the field of view likely to pass the instrumental filter at exo-Earth level.

Stellar limb darkening is shown to cause bias in leakage calibration if unaccounted for. Occurrence of perturbing background stars or galaxies in the typical FOV is unlikely. We extract galactic interstellar medium background emissions for current target lists. Galactic background can be considered uniform over the FOV, and it should show no significant drift with parallax. Our model specifications have been embedded into a Java simulator, soon to be made open-source. We have also designed an associated FITS input/output format standard that we present here.

Abstract: In addition to fitting the data of 233 extra-solar planets with power laws, we construct a correlated mass-period distribution function of extrasolar planets, as the first time in this field. The algorithm to generate a pair of positively correlated beta-distributed random variables is introduced and used for the construction of correlated distribution functions. We investigate the mass-period correlations of extrasolar planets both in the linear and logarithm spaces, determine the confidence intervals of the correlation coefficients, and confirm that there is a positive mass-period correlation for the extrasolar planets. In addition to the paucity of massive close-in planets, which makes the main contribution on this correlation, there are other fine structures for the data in the mass-period plane.

Abstract: A Bayesian multi-planet Kepler periodogram has been developed for the analysis of precision radial velocity data (Gregory 2005b and 2007). The periodogram employs a parallel tempering Markov chain Monte Carlo algorithm. The HD 11964 data (Butler et al. 2006) has been re-analyzed using 1, 2, 3 and 4 planet models. Assuming that all the models are equally probable a priori, the three planet model is found to be greater than 600 times more probable than the next most probable model which is a two planet model. The most probable model exhibits three periods of 38.02+0.06-0.05, 360+-4 and 1924+44-43 d, and eccentricities of 0.22+0.11-0.22, 0.63+0.34-0.17 and 0.05+0.03-0.05, respectively. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass (M sin i) and semi-major axis are 0.090+0.15-0.14 M_J, 0.253+-0.009 au, 0.21+0.06-0.07 M_J, 1.13+-0.04 au, 0.77+-0.08 M_J, 3.46+-0.13 au, respectively. The small difference (1.3 sigma) between the 360 day period and one year suggests that it might be worth investigating the barycentric correction for the HD 11964 data.

Abstract: In recent years we have witnessed an explosion of photometric time-series data, collected for the purpose of finding a small number of rare sources, such as transiting extrasolar planets and gravitational microlenses. Once combed, these data are often set aside, and are not further searched for the many other variable sources that they undoubtedly contain. To this end, we describe a pipeline that is designed to systematically analyze such data, while requiring minimal user interaction. We ran our pipeline on a subset of the Trans-Atlantic Exoplanet Survey dataset, and used it to identify and model 773 eclipsing binary systems. For each system we conducted a joint analysis of its light curve, colors, and theoretical isochrones. This analysis provided us with estimates of the binary’s absolute physical properties, including the masses and ages of their stellar components, as well as their physical separations and distances. We identified three types of eclipsing binaries that are of particular interest and merit further observations. The first category includes 11 low-mass candidates, which may assist current efforts to explain the discrepancies between the observation and the models of stars at the bottom of the main-sequence. The other two categories include 34 binaries with eccentric orbits, and 20 binaries with abnormal light curves. Finally, this uniform catalog enabled us to identify a number of relations that provide further constraints on binary population models and tidal circularization theory.

Comments: 64 pages, 23 figures, accepted for publication in AJ, see this http URL for the catalog

Abstract: Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that analytical machinery with numerics. The resulting semianalytical theory is then applied to Deimos over long time scales. In parallel, we carry out a purely numerical integration in an inertial Cartesian frame. The results agree to within a small margin, for over 10 Myr, demonstrating the applicability of our semianalytical model over long timescales. This will enable us to employ it at the further steps of the project, enriching the model with the tides, the pull of the Sun, and the planet’s triaxiality. Another goal of our work was to check if the equinoctial precession predicted for a rigid Mars could have been sufficient to repel the orbits away from the equator. We show that for low initial inclinations, the orbit inclination reckoned from the precessing equator of date is subject only to small variations. This is an extension, to non-uniform precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession and a low initial inclination. However, near-polar initial inclinations may exhibit considerable variations for up to +/- 10 deg in magnitude.

Nevertheless, the analysis confirms that an oblate planet can, indeed, afford large variations of the equinoctial precession over hundreds of millions of years, without repelling its near-equatorial satellites away from the equator of date: the satellite inclination oscillates but does not show a secular increase. Nor does it show secular decrease, a fact that is relevant to the discussion of the possibility of high-inclination capture of Phobos and Deimos.

Abstract: The role of radial velocity (RV) jitters in extrasolar planet search surveys is discussed. Based on the maximum-likelihood principle, improved statistical algorithms for RV fitting and period search are developed. These algorithms incorporate a built-in jitter determination, so that resulting estimations of planetary parameters account for this jitter automatically. This approach is applied to RV data for several extrasolar planetary systems. It is shown that many RV planet search surveys suffer from periodic systematic errors which increase effective RV jitters and can lead to erratious conclusions. For instance, the planet candidate HD74156 d may be a false detection made due to annual systematic errors.

Charter

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last seven years, this site has coordinated its efforts with the Tau Zero Foundation, and now serves as the Foundation's news forum. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image: Marco Lorenzi).

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